Geometric applications of harmonic maps

Jürgen Jost
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Jürgen Jost: Ruhr-Universität Bochum, Mathematisches Institut

Chapter 5 in Nonlinear Methods in Riemannian and Kählerian Geometry, 1991, pp 125-146 from Springer

Abstract: Abstract In this section, we shall use our Bochner type formula (3.2.10), 5.1.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdq0aaW % baaSqabeaacqGHsislaaGccaWGLbGaaiikaiaadAgacaGGPaGaeyyp % a0ZaaqWaaeaacqGHhis0caWGKbGaamOzaaGaay5bSlaawIa7amaaCa % aaleqabaGaaGOmaaaakiabgUcaRmaalaaabaGaaGymaaqaaiaaikda % aaGaeyipaWJaamizaiaadAgacqGHflY1caqGsbGaaeyAaiaabogada % ahaaWcbeqaaiaad6eaaaGccaGGOaGaamyzamaaBaaaleaacqaHXoqy % aeqaaOGaaiykaiaacYcacaWGKbGaamOzaiabgwSixlaadwgadaWgaa % WcbaGaeqySdegabeaakiabg6da+iabgkHiTmaalaaabaGaaGymaaqa % aiaaikdaaaGaeyipaWJaamOuamaaBaaaleaacaWGnbaabeaakiaacI % cacaWGKbGaamOzaiabgwSixlaadwgadaWgaaWcbaGaeqySdegabeaa % kiaacYcacaWGKbGaamOzaiabgwSixlaadwgadaWgaaWcbaGaeqOSdi % gabeaakiaacMcacaWGKbGaamOzaiabgwSixlaadwgadaWgaaWcbaGa % eqOSdigabeaakiaacYcacaWGKbGaamOzaiabgwSixlaadwgadaWgaa % WcbaGaeqySdegabeaakiabg6da+aaa!809A! $${\Delta ^ - }e(f) = {\left| {\nabla df} \right|^2} + \frac{1}{2} - \frac{1}{2} $$ for a harmonic f: N → M in order to derive some elementary results about the topology of nonpositively curved Riemannian manifolds. These results are well-known, and the present section therefore is included only for reasons of exposition.

Keywords: Riemannian Manifold; Sectional Curvature; Closed Geodesic; Isometric Immersion; Compact Riemann Surface (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-3-0348-7706-0_5

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